The First Magnitude Stars Table lists the brighest stars in the sky that are -1, 0 and 1 magnitude. Sirius is the brighest at -1.44 magnitude. These stars are refered to as First Magnitude stars since they are all 1 magnitude or brighter.
Brightness of stars are assigned a number starting with the brightest star Sirius starting at -1.44 magnitude. Dimmer stars are positive numbers. The larger the number means the dimmer the star is. For example, a star -1 magnitude is brighter than a star 0 magnitude. A star 0 magnitude is brighter than a star 1 magnitude. A star 1 magnitude is brighter than a star 2 magnitude. Magnitude sequence for stars starting with the brightest is -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 magnitude, ... etc.
Star names come from Greek, Latin and Arabic origins. For example, Sirius and Capella are of Greek and Latin origns and Vega, Rigel, Aldebaran are Arabic derivations. In some cases two names are given to a star because some stars are refered to with multiple names.
The designation column gives the star's designation by Johann Bayer's letter and John Flamsteed's number.
Johann Bayer's Uranometer star maps (1603) introducted the designating the brighter stars of each constellation by small letters of the Greek alphabet.

In general, the stars are lettered in order of brightness. In a constellation the brightnest star is Alpha, the second brightest Beta and so on. That is why most of the First Magnitude Stars are designated Alpha and a few are designated Beta. The full name of the star in the Johann Bayer system is the letter followed by the genitive (possessive) of the Latin name of the constellation. For example, Sirius is Alpha Canis Majoris. The below table uses the constellation abbreviations. Therefore, Sirius designation is Alpha CMa.
A different plan used in John Flamsteed's Historia Coelestis (1729). The stars are numbered consecutively from west to east across the constellation. Therefore, in the John Flamsteed system Sirius is designated 9 Canis Majoris.
In the Magnitude column the letter "c" refers to the combined magnitude of a double star and "v" refers to the median magnitude of a variable star. Star magnitude data is from the Hipparcos Catalog
First Magnitude Stars Table

Name	Designation	Magnitude
Sirius	9 Alpha CMa	-1.44
Canopus	Alpha Car	-0.62
Rigil Kent or Alpha Centauri	Alpha Cen	-0.28c
Arcturus	16 Alpha Boo	-0.05v
Vega	3 Alpha Lyr	0.03v
Capella	13 Alpha Aur	0.08v
Rigel	19 Beta Ori	0.18v
Procyon	10 Alpha CMi	0.40
Achernar	Alpha Eri	0.45v
Betelgeuse or Betelgeux	58 Alpha Ori	0.45v
Agena or Hadar	Beta Cen	0.61v
Altair	53 Alpha Aql	0.76v
Acrux	Alpha Cru	0.77c
Aldebaran	87 Alpha Tau	0.87
Spica	67 Alpha Vir	0.98v
Antares	21 Alpha Sco	1.06v
Pollux	78 Beta Gem	1.16
Fomalhaut	24 Alpha PsA	1.17
Beta Crucis	Beta Cru	1.25v
Deneb	50 Alpha Cyg	1.25v
Regulus	32 Alpha Leo	1.36